Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 1.7 Junior Find the answer

If $4^{n}=64^{2}$ , what is the value of $n$ ?

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

We note that $64=4 \times 4 \times 4$ . Thus, $64^{2}=64 \times 64=4 \times 4 \times 4 \times 4 \times 4 \times 4$ . Since $4^{n}=64^{2}$ , then $4^{n}=4 \times 4 \times 4 \times 4 \times 4 \times 4$ and so $n=6$ .

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